EXCHANGE 


I A  Study  of  the  Vapor  Pressure  Lowering  of 
Aqueous  Solutions  of  Mannite  at  20°  C* 


DISSERTATION 


SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES  OF  THE 

JOHNS  HOPKINS  UNIVERSITY  IN  PARTIAL  FULFILLMENT 

OF  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 


BY 
THOMAS  HUNTON  ROGERS 


BALTIMORE,  MD. 
June,  1917 


*  2y  *sf  **. 


EASTON,  PA.; 

ESCHENBACH  PRINTING  COMPANY 
1920 


A  Study  of  the  Vapor  Pressure  Lowering  of 
Aqueous  Solutions  of  Mannite  at  20°  C 


DISSERTATION 


SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES  OF  THE 

JOHNS  HOPKINS  UNIVERSITY  IN  PARTIAL  FULFILLMENT 

OF  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 


BY 

THOMAS  HUNTON  ROGERS 

BALTIMORE,  MD. 

June,  1917 


EASTON,  PA.: 

ESCHENBACH  PRINTING  COMPANY 
1920 


> 


\o 


CONTENTS. 

Acknowledgment 4 

Introduction 5 

Experimental : 

Series  1 6 

Observations 6 

Data 7 

Series  II 9 

Preparation  of  Solutions 9 

Observations 10 

Analysis  of  Solutions 1 1 

Data 12 

Discussion  of  Results : 

Accuracy  of  Method 19 

Raoult's  Law 19 

Von  Babo's  Law  and  Heat  of  Dilution 21 

Vapor  Pressure  and  Osmotic  Pressure 24 

Summary 24 

Biography 25 


462002 


ACKNOWLEDGMENT. 

The  author  is  indebted  to  Professors  Remsen,  Morse,  Reid,  the  late 
Professor  Jones,  and  to  Drs.  Bateman  and  Shenton  for  instruction  in 
the  lecture  room  and  laboratory. 

He  is  also  especially  grateful  to  Professors  Frazer  and  Lovelace,  under 
whose  guidance  the  investigation  was  carried  out,  for  their  valuable  sug- 
gestions and  assistance  throughout  the  work. 


A  STUDY  OF  THE  VAPOR  PRESSURE  OF  AQUEOUS  SOLUTIONS 

OF  MANNITE. 
Introduction. 

The  vapor  pressure  method  offers  certain  advantages  for  the  investiga- 
tion of  the  colligative  properties  of  solutions,  and,  though  many  efforts 
have  been  made  to  apply  it  to  the  study  of  aqueous  solutions,  the  results 
have  not  been  entirely  successful.  The  fundamental  importance  of  the 
knowledge  of  the  vapor  pressure  of  solutions  is  shown  by  its  frequent 
use  in  thermodynamic  formulas.  In  practice  2  methods,  known  as  the 
dynamic  and  static  methods,  have  been  used.  The  first  depends  on  the 
determination  of  the  amount  of  the  solvent  required  to  saturate  the  same 
volume  of  air  when  in  equilibrium  with  the  solvent  and  solution,  respec- 
tively, both  maintained  at  the  same  constant  temperature.  This  method 
has  been  used  by  Ostwald;  the  Earl  of  Berkeley1  and  his  associates  have 
investigated  the  various  sources  of  error  involved  in  this  method  andi 
have  made  many  improvements  in  the  apparatus  and  details  of  manipula^ 
tion.  The  recent  work  of  Washburn2  has  been  essentially  an  applica- 
tion of  the  apparatus  of  Berkeley. 

Some  time  ago  Frazer  and  Lovelace,3  in  spite  of  the  failure  of  earlier 
workers,  described  an .  apparatus  and  manipulation  by  which  accurate 
measurements  of  vapor  pressure  of  aqueous  solution  by  the  static  method 
could  be  made.  Many  of  the  errors  which  had  previously  been  encoun- 
tered in  attempting  to  apply  this  method  were  eliminated  by  making 
it  differential,  comparing  directly,  by  means  of  the  Rayleigh  manometer, 
the  vapor  pressures  above  the  solution  and  the  pure  solvent  when  both 
were  maintained  in  the  same  accurately  regulated  thermostat. 

After  preliminary  work  certain  improvements  were  made  in  the  tem- 
perature regulation  and  the  method  of  stirring,  and  the  method  was  ap- 
plied to  the  study  of  aqueous  solutions  of  mannite.  After  the  elimina- 
tion of  certain  other  slight  sources  of  error  the  method  was  extended  to 
aqueous  solutions  of  potassium  chloride.4 

The  present  paper  is  a  repetition  of  the  study  of  mannite  solutions  in 
the  course  of  which  an  additional  slight  source  of  error  was  discovered 

1  Proc.  Roy.  Soc.,  (A).  17,  156  (1906). 

2  Washburn,  /.  Am.  Chem.  Soc.  37,  309  (1915). 

3  Frazer  and  Lovelace,  ibid.,  36,  2439  (1914);  Z.  physik.  Chem.,  89,  155  (1914). 

4  Lovelace,  Frazer  and  Miller,  /.  Am.  Chem.  Soc.,  38,  515  (1916). 


and  eliminated.  The  work  on  potassium  chloride  solutions  was  also  re- 
peated, the  results  of  which  will  be  the  subject  of  a  future  communica- 
tion. 

Experimental. 

Series  I. — The  apparatus  used  for  this  work  was  that  described  in 
the  work  on  potassium  chloride  solutions.1  The  mannite  used  was  care- 
fully purified  and  the  same  sample  used  throughout.  The  experimental 
details  were  carried  out  in  this  series  in  practically  the  same  manner  as 
in  the  previous  work.  The  solutions  were  subjected  to  a  preliminary 
removal  of  air  by  repeatedly  exhausting  the  space  above  the  solution  con- 
tained in  a  specially  constructed  flask  as  there  described,  and  were  further 
freed  from  air  after  they  were  introduced  into  the  bath.  Often  the  vapor 
was  allowed  to  expand  into  an  evacuated  bulb  as  many  as  25  times  be- 
fore the  solution  was  sufficiently  air-free  to  take  observations.  The  test 
for  air  was  made  by  measuring  with  the  McLeod  gage  the  residual  pressure 
after  the  liter  bulb,  which  contained  the  vapor  from  the  solution,  had 
been  opened  to  the  flask  containing  phosphorus  pentoxide. 

To  insure  equilibrium  between  liquid  and  vapor  phase  before  testing, 
the  solution  was  left  open  to  the  vapor  bulb  for  24  hours  with  intermittent 
stirring  of  the  solution.  When  the  test  was  made,  it  was  observed  that 
while  practically  all  the  vapor  seemed  to  be  absorbed  in  perhaps  a  half 
hour,  a  further  slow  absorption  took  place  for  a  number  of  hours.  At 
the  end  of  about  12  hours  the  reading  on  the  gage  became  constant  and, 
if  the  pressure  indicated  was  0.0005  mm-  or  less»  tne  test  was  considered 
satisfactory  and  the  air  present  deemed  negligible.  While  this  behavior, 
especially  the  slowness  of  the  absorption,  occasioned  surprise,  its  sig- 
nificance was  entirely  overlooked  during  this  series. 

Observations. — A  careful  study  was  made  of  the  proper  conditions 
for  taking  observations.  In  the  light  of  the  previous  work  it  was  obvious 
that  an  essential  condition  is  that  the  temperature  of  the  room  should  be 
fairly  constant.  As  the  work  progressed,  however,  it  was  found  un- 
necessary to  provide  for  any  special  regulation  of  the  temperature  of  the 
room,  though  it  is  necessary,  of  course,  to  prevent  any  sudden  change. 
Under  these  conditions  evaporation  and  condensation  at  the  surface 
of  the  solvent  and  solutions  are  sufficiently  rapid  to  prevent  any  dis- 
turbance in  the  pressure  of  the  system  caused  by  the  slow  fluctuations 
of  the  room  temperature. 

After  removal  from  the  bath  the  solutions  were  analyzed  both  by  the 
use  of  the  interferometer  and  by  evaporating  a  weighed  portion  to  dry- 
ness  and  heating  the  residue  to  constant  weight  at  130°.     The  results 
of  the  2  methods  accorded  well. 
1  Loc.  tit. 


Table  I  gives  in  brief  the  results  of  this  (preliminary)  investigation  of 
the  lowerings  of  mannite  solutions  of  10  different  concentrations.  Col- 
umn i  gives  the  concentrations  expressed  in  mols  (O  =  16)  of  solute 
per  looo  g.  of  solvent.  Column  3  gives  the  lowerings  produced  in  mm. 
of  mercury  at  the  prevailing  room  temperature.  For  the  sake  of  com- 
parison, Column  2  gives  the  lowerings  found  by  Mullikin1  expressed  simi- 
larly. His  data  have  been  extrapolated  over  a  slight  range  in  order  to 
get  values  corresponding  to  the  concentrations  in  Column  i. 

Column  4  shows  the  theoretical  lowerings  of  these  solutions  as  calcu- 
lated from  Raoult's  law,  and  under  the  same  conditions  as  the  values  in 
Columns  2  and  3.  Column  5  gives  the  deviations  from  Raoult's  law 
of  the  values  found  in  this  series. 

TABI^E  I. 
Comparison  of  the  Values  Obtained  for  the  Lowering  of  Mannite  Solutions. 


M. 

Mullikin. 

Series  I. 

Calculated. 

Difference. 

Series  II. 

0.0995 

0.0287 

0.0280 

0.0314 

0.0034 

0.03II 

0.1993 

o  .  0587 

0.0585 

0.0627 

0.0042 

O.o62O 

0.2985 

o  .  0906 

0.0882 

0.0939 

0.0057 

o  .  0930 

0.3984 

O.II88 

O.I22I 

O.I25I 

0.0030 

0.1239 

o  .  4986 

0.1538 

0.1533 

0.1563 

0.0030 

0.1553 

0.5968 

0.1819 

0.1867 

0.0048 

0.1869 

o  .  6960 

0.2127 

0.2175 

0.0048 

0.2173 

0.7958 

.  . 

0.2471 

0.2489 

O.OOlS 

0.2491 

0.8944 

.  . 

0.2740 

0.2784 

0.0044 

0.2802 

0.9941 

0.3061 

0.3088 

0.0027 

0.3108 

Column  6  gives  the  values  found  in  Series  II  (vide  infra)  extrapolated 
and  expressed  similarly. 

The  agreement  of  the  results  in  Series  I  with  those  of  Mullikin  is  fair, 
though  in  several  cases  there  is  greater  deviation  than  the  o.ooi  mm. 
claimed  as  the  accuracy  of  the  method.  However,  the  nearly  constant 
deviation  from  Raoult's  law  was  suspicious,  especially  in  the  concentra- 
tions where  the  best  agreement  would  be  expected.  In  order  to  make 
certain  that  the  solutions  measured  were  free  from  air  another  method 
of  preliminary  removal  of  air  was  devised.  This  will  be  described  when 
the  discussion  of  the  results  of  Series  II  is  taken  up.  It  was  found  that 
solutions  so  prepared  gave  a  lowering  from  0.003  to  0.005  mm-  greater 
than  those  recorded  in  Series  I.  Further,  when  tests  for  air  were  made 
on  the  solutions  of  Series  II,  the  readings  on  the  McLeod  gage  showed 
negligible  air  pressure  after  20  minutes  absorption  by  the  phosphorus 
pentoxide.  This  difference  in  behavior  was  obviously  due  to  the  fact 
that  the  solutions  of  Series  I  were  measured  with  an  air  pressure  of  o .  003- 
0.005  mm-  The  gage  readings  on  air  tests  should  have  been  made  after 
the  same  length  of  time,  20  minutes,  whereupon  the  air  present  would 
1  R.  Mullikin,  Dissertation,  Johns  Hopkins  Univ.,  1916. 


8 


have  been  discovered.  If  the  pentoxide  is  kept  open  for  a  longer  time,  ad- 
sorption of  the  residual  air  takes  place  slowly,  both  by  the  pentoxide 
and  the  glass  surfaces1  of  the  system.  The  agreement  between  Mullikin's 
results  and  those  of  Series  I  is  better  than  might  be  expected  since  the 
solutions  in  Series  I  were  measured  with  an  air  pressure  of  about  0.004 
mm.  But  this  residual  amount  of  air  pressure  was  practically  the  same 


FIG  1 


in  each  case  since  the  same  methods  of  preparation  of  solutions  were 
used  and  the  same  criterion  adopted  for  testing  the  presence  of  air,  the 
result  being  that  nearly  the  same  amount  of  air  was  left  in  practically 
every  case. 

1  Menzies,  /.  Am.  Chem.  Soc.,  42,  978  (1920). 


Series  II.  Preparation  of  the  Solutions. — In  order  that  the  solutions 
might  be  made  up  to  a  definite  concentration  it  seemed  best  to  have 
both  solvent  and  solute  free  from  air  and  mix  the  two  in  a  vacuum.  After 
several  trials  a  method  was  found  which  accomplished  this  in  a  satisfac- 
tory manner. 

The  water  is  introduced  into  a  5oo-cc.  flask  A,  Fig.  i,  to  which  is  sealed 
a  length  of  7  mm.  glass  tubing.  A  constriction  a  is  drawn  near  the  end 
of  the  tube  and  a  short  piece  of  rubber  tubing  fitted  on  the  end.  After 
boiling  the  water  vigorously  for  30-35  minutes,  the  rubber  tube  is  sud- 
denly pinched  shut,  at  the  same  time  removing  the  burner.  The  tube  is 
then  quickly  sealed  off  at  the  constriction.  The  flask  having  been  pre- 
viously weighed,  by  weighing  the  sealed  flask  and  tip  the  amount  of  water 
contained  is  determined. 

A  short  length  of  tubing  is  sealed  to  the  neck  of  a  3oo-cc.  flask  and 
another  into  the  bottom,  as  shown  in  B,  Figs,  i  and  2.  An  amount  of 
solute  corresponding  to  the  weight  of  water  prepared  is  introduced  in 
the  flask.  After  making  a  file  mark  on  the  tip,  the  tube  of  the  flask  con- 
taining the  water  is  joined  to  one  end  of  the  flask  B  by  means  of  a  stout 
rubber  tube,  as  shown  in  Fig  2,  and  the  other  end  is  connected  to  a  vacuum 
pump.  The  solute  is  thus  freed  from  air  after  several  hours  pumping. 
Finally  the  tube  connecting  to  the  pump  is  sealed  off  at  b  and  the  solute 
and  solvent  mixed  by  breaking  the  tip  of  the  flask  A  inside  the  connecting 
rubber  tube.  After  solution  is  effected,  the  rubber  tube  is  pinched  shut, 
the  flask  A  removed  and  a  specially  constructed  pipet,  p,  Fig.  3,  put  in 
its  place.  A  file  scratch  is  made  on  the  other  end  of  the  flask  now  free 
and  connection  made  to  a  mercury  reservoir  as  shown.  To  introduce 
the  solution  this  tip  is  broken  under  the  mercury  and  the  end  of  the  pipet 
placed  under  the  bottom  of  the  tube  which,  dipping  in  mercury,  leads 
up  into  the  temperature  bath.1  Under  pressure  from  the  reservoir  the 
solution  flows  out  of  the  flask  and  bubbles  up  through  the  mercury  to 
the  reservoir  in  the  bath. 

Solutions  prepared  and  introduced  in  this  manner  require  only  a  few 
vapor  expansions  in  the  bath  in  order  to  remove  the  air  completely.  The 
use  of  rubber  tubing  for  a  connection  in  the  apparatus  cannot  be  con- 
veniently avoided  and  no  trouble  from  leakage  was  experienced  after  a 
good  grade  of  antimony  rubber  tubing  had  been  selected  and  care  taken 
to  wire  the  end.  Absolutely  complete  removal  of  air  in  the  preparation 
of  a  solution  was  not  attempted,  as  there  is  always  some  air  taken  up  in 
introducing,  due  to  the  slight  amount  of  air  trapped  by  the  mercury  col- 
umn on  the  walls  of  the  tubes  leading  up  into  the  bath.  The  flask  in 
which  the  water  was  boiled  was  steamed  out  thoroughly  before  using. 
After  this  a  sample  of  water  which  had  been  boiled  in  the  flask  for  35 
1  See  Fig.  i,  /.  Am.  Chem.  Soc.,  38,  517  (1916). 


10 

minutes  was  compared  in  the  interferometer  with  a  sample  of  conductivity 
water.  The  difference  in  density  was  found  to  be  very  slight  and  cer- 
tainly not  enough  impurities  were  present  to  effect  a  lowering  of  the  vapor 
pressure.  In  this  work  either  conductivity  water  or  distilled  water,  which 
compared  favorably  in  the  interferometer  with  conductivity  water,  was 
used  throughout. 

Observations. — The  readings  were  taken  under  conditions  as  de- 
scribed in  Series  I.  Frequently  observations  were  attempted  before  the 
solutions  were  air-free,  as  in  this  way  the  rate  of  the  removal  of  air  could 
be  followed.  Hence  these  preliminary  readings  were  not  reliable  and  no 
results  are  recorded  here  unless  the  solutions  had  been  shown  to  have  less 
than  0.0004  mm.  residual  air  pressure.  The  exact  reading  of  the  McLeod 
gage  is  unsatisfactory  at  this  slight  pressure,  but  it  is  safe  to  say  that  the 
maximum  air 'pressure  of  a  solution  considered  air-free  was  as  small  as 
this  amount,  while  generally  it  was  much  less.  At  the  time  of  making 
readings  the  residual  air  was  certainly  less,  for  the  solution  and  solvent 
were  subjected  to  a  fresh  vapor  expansion  just  before  observations  were 
made. 

Constant  readings  can  be  obtained  within  15  minutes  after  opening 
a  solution  to  an  evacuated  bulb.  If  appreciable  air  were  present  in  the 
solution  the  deflection  would  not  be  constant,  due  to  air  coming  out  of 
the  solution  gradually.  This  phenomenon  was  actually  observed  in 
many  preliminary  observations  on  solutions  known  to  contain  air,  when 
the  readings  would  gradually  drop.  When  the  solution  is  once  freed 
from  air  no  trouble  is  experienced  in  getting  a  series  of  concordant  meas- 
urements. 

The  observations  were  continued  until  at  least  5  consecutive  concordant 
sets  were  obtained.  In  these  final  measurements  as  recorded  here  no 
values  have  been  discarded  unless  the  data  were  unreliable  for  obvious 
reasons,  such  as  the  loss  of  the  zero  point,  or  a  change  in  bath  tempera- 
ture. A  few  non-concordant  values  are  bracketed.  Some  readings 
were  taken  while  the  solutions  were  being  stirred  at  a  variable  speed 
and  the  deflections  were  found  to  be  independent  of  the  rate  of  stirring, 
so  that  practically  all  of  the  observations  were  made  with  constant  speed 
stirring.  The  arrangement  mentioned  was  such  that  the  rate  of  stirring 
was  changed  over  a  wide  range  several  times  each  minute,  thus  effectually 
preventing  surface  concentration. 

The  zero  point  of  the  measurement  is  given  by  the  setting  of  the  manom- 
eter when  the  limbs  of  this  instrument  are  open  to  one  another.  This 
reading  was  always  taken  before  and  after  each  reading  of  the  deflec- 
tion. Sornetimes  due  to  the  slight  unsteadiness  of  the  telescope  mount- 
ing, the  zero  value  was  not  checked.  In  such  cases  the  deflection  was 


11 

taken  again.  If  the  2  values  checked,  these  2  deflections  together  with 
the  included  zero  point,  were  used  to  compute  the  lowering. 

To  calculate  the  lowering,  the  scale  deflection,  s,  the  distance  between 
the  points  of  the  manometer,  d,  and  the  distance  from  the  mirror  on  the 
manometer  to  the  scale  D,  must  be  known.  The  lowering,  h,  is  given 
by  the  expression1  h  =  d/2D  s  or,  h  =  ks.  This  involves  the  assump- 
tion that  sin  6  =  l/2  tan  26,  where  6  is  the  angle  of  tilt  of  the  manometer. 
This  assumption  is  found  not  to  introduce  an  appreciable  error  in  the 
case  of  the  most  concentrated  solution  investigated  here.  The  value  of 
d  for  the  manometer  was  redetermined  and  the  length,  D,  was  frequently 
checked.  The  value  of  h  thus  calculated  is  the  height  of  a  column  of 
mercury  at  room  temperature,  about  24°.  This  is  corrected  to  the  height 
of  a  column  of  mercury  at  o°,  which  is  the  lowering  pQ  —  pi. 

Analysis. — After  taking  due  precaution  to  keep  the  solution  as  near  as 
possible  to  the  original  concentration  in  removing  it  from  the  bath,  the 
-exact  concentration  was  determined.  The  Rayleigh-Zeiss  interferometer 
served  admirably  for  this  purpose.  With  a  20  mm.  cell  a  solution  can 
be  compared  with  a  standard  with  as  great  an  accuracy  as  that  with  which 
the  standard  can  be  prepared.  By  making  a  rough  analysis  and  then 
preparing  a  standard  of  very  nearly  the  concentration  of  the  solution  being 
analyzed  the  interferometer  serves  practically  as  a  zero  instrument. 
Often  as  a  check  the  weighed  portion  of  a  solution  was  evaporated  to 
dryness  and  the  residue  dried  to  a  constant  weight  at  130°.  These  re- 
sults accorded  well  with  those  from  the  interferometer  method.  No 
trouble  was  experienced  in  getting  a  constant  weight  of  the  mannite 
residue,  a  difficulty  mentioned  by  Flugel.2  The  molar  concentration 
was  thus  easily  determined  with  an  accuracy  of  2  X  io~4  weight  molar, 
which  corresponds  to  a  vapor  pressure  lowering  of  less  than  o.oooi  mm. 
The  concentration  was  always  expressed  in  terms  of  mols  of  mannite 
per  1000  g.  of  water,  the  weights  being  reduced  to  the  vacuum  standard, 
and  182 . 12  employed  as  the  molecular  weight  of  mannite. 

RESULTS. 
0.09845  M  Mannite. 

Date.  Zero.  Reading.  Zero.         Deflection  (mean). 

II/8/I6  I.I  7-2 

1.0  7-0 

0-95  7-i  0.95 

i.o  6.10 

11/9/16  i.o  7.1 

1.05  7.05  1.05 

7.1  i.i  6.01 

1J.  Am.  Chem.  Soc.,  36,  2440  (1914). 

*  Fliigel,  Z.  physik.  Chem.,  79,  577  (1912). 


12 

0.08845  M  Mannite  (Continued}. 


Date. 

11/9/16 


11/10/16 


11/11/16 


11/11/16 


Zero. 

1-9 
1.8 

1.75 

1.8 
0.95 

I.O 

2  .O 
2.0 


2.8 
2.8 

2.9 


Reading. 

7-9 

7-9 

7-95 

7.0 

7-0 

7.0 

8.1 

8.15 

8.0 

8.1 

8.9 

8.95 

8.85 


Zero. 


1.8 
1-7 

I.O 

0-95 


2.05 
2.05 

2.8 
2.9 


Deflection  (mean). 


6. ii 


6.02 


6.08 


6.06 


Average  deflection 6.06  ram. 

Lowering  (corr.  to  Hg  at  o°) =  o .  0307  mm. 

Maximum  deviation =  0.0005  mm. 

k  =  0.005080 


0.1977  M  MANNITE. 

Date.  Zero.  Reading.  Zero.  Deflection. 

10/27/16 3.6        15.7  ... 

3-6       15.85 

15-8       3.6       12. 18 

10/28/16 14  .o 

1-95      14-0 

14.05        2 .O         12 .04 

10/29/16 i.o      13.15      i.o 

1-05        13-2         1.05 

13.1      i.o      12.13 

IO/30/I6... 3.0         15.1 

3-0      15.15  2.95 

15.05  3.0      12. ii 

11/1/16 2.9      15.0 

2.8       14.95  3.0 

2.85      15.0  3.0      12.13 

II/I/I6.., 2.1         14.15 

2  .05        14.1  .  .  ... 

14-2  2.05 

14-2  2.05        12.10 

II/4/I6 . 3.05        15.1 

3-05        I5-I  2.95 

I5-05      3-0       12.07 

Average  deflection 12.11 

Lowering  (corr.) =o  .0614  rnm. 

k  —  0.005080 


13 


0.2962  M  MANNITE. 


Date. 
II/8/I6      

Zero. 
I    I 

Reading. 

Zero. 

II/9/I6  

I  .0 

0-95 
i  .0 
.  .  .  .      19 

19    1.5 
19.2 

19.15 

0.95 

I  .0 

i  1/10/16  .         .        ... 

1.8 

1-75 
1.8 
o  0=; 

20.0 
19   95 
19  95 

10    2 

i  9 
1.8 
i? 

i  i/i  1/16       . 

I  .0 
I    OS 

19.2 
19-2 
2O    2 

I  .0 

0.95 

11/11/16 

2  .0 
2    8 

2O.  I 
20.05 
20.2 
2  1    OS 

2  .0 
2  .O 

Average  deflection.  .  .  . 

2.9 

21  .0 
21  .0 

2.8 

2.9 

Lowering  (corr.) 

o  0922  mm 

k  =  0.005080 

Date 
11/18/16  

0.3949  M 
Zero. 

MANNITE. 

Reading. 
26   7 

Zero. 

11/18/16     . 

2    I 

26.65 
26.65 
26.6 

26  ^s 

2-5 
2-5 

11/19/16 

2  .1 
I    IS 

26  .2 
26.25 
2S    2S 

2  .1 

1  1/20/16        .  .                  .    . 

1.05 
I  .1 
2    OS 

25-3 
25-3 
27    I  S 

1-05 
1.05 

11/20/16  . 

3-0 

2    7 

27.15 
27.1 

26  o 

2-95 

Average  deflection  

2.7 

26  .9 
26.85 

2.65 

Lowering  (corr.)  .  . 

0.1227  mm. 

Deflection. 


18.17 


18.16 


18.22 


18.15 


Deflection. 


24.15 


24.17 


24.20 


24.16 


24.20 


24. 1 8  mm. 


0,005080 


14 
0.4938  M  Mannite. 

Date.  Zero.  Reading.  Zero.  Reading.      Deflection  (mean). 

I2/I/I6  290.05  320.1 

290.0  320.1  289.95  320.1 

290.05  320.05  289.95  320.15  30.15 

I2/2/I6  ..  320.7  290.45  320.6 

320.7  290.5  320.75 

320.7  290.5  320.75  30.22 

I2/2/I6  290.8  321.0 

290.8  321.0  290.8 

321.0  290.85        ..          30.19 
I2/2/I6     290.4      320.55 

290.4  320.55  290.4 

320.5       290.4  30.13 

I2/3/I6     290.0      320.35 

290.05  320.3 

320.3  290.0  ...  30.31 

Average  deflection 30. 20  mm. 

Lowering  (corr.) =  o.  1542  mm. 

Maximum  deviation =  0.0007  mm. 

k  =  0.005109 

0.5944  M  MANNITE. 

Zero.  Deflection. 


289.3 
289.3 
289.3  36.54 

289.35 

289.3         36.54 


289.4         36.59 


295.2 

295.25       36.60 


295.75       36.55 


295.0         36.55 

Average  deflection 36 . 56  mm. 

Lowering  (corr.) ,,..,,, '     o .  1860  mm. 

k  =  0.005109 


Date. 

Zero. 

Reading. 

I2/IO/l6 

289.2 

325  -9 

289.2 

325.8 

325.8 

325.7 

325.8 

I2/IO/I6  

289.3 

325.85 

289.3 

325.8 

289.3 

325.9 

I2/IO/I6  

289.5 

326.0 

289-4 

326.0 

326.05 

I2/I  I/l6  

295  .2 

331  .85 

295-1 

331-8 

295-2 

33i  -75 

331-75 

I2/II/I6  

295.7'- 

332.35 

295-7 

332.25 

295-75 

332.25 

332.15 

J2/I  I/l6    

.......     295  o 

33  1  -6 

295.0 

331-5 

331-55 

15 


Date. 
I2/l6/l6 

0.5958  M  MA 

Zero. 
291    9 

.NNITE. 
Reading. 

328.5 
328.5 
328.6 
328.65 
328.7 
328.6 
328.6 
328.75 
328.8 
328.75 
322.95 
329.45 
329.55 
329.6 
329.45 
329.35 
329.3 
329.35 
328.75- 
328.8 
328.8 
329.15 
329.2 
329    15 
328.5 
328.55 
328.5 
328.6 

Zero. 

291.9 
291  .9 

292  .0 

292  .O 

292.0 
292  .O 

292.9 

292.85 

292  .85 

292  .25 
292.25 

292.5 
292  .5 

292  .O 
291  .9 

Deflection. 
36.63 

36.66 
36.77 

36.68 

36.49 
36.55 
36.70 

36.60 

I2/l6/l6 

291  .9 
291  .95 

I2/I7/l6 

291  .9 
292  .O 

292  .O 
292  .0 
292  .85 

I2/l8/l6  

292  .85 
292  .85 

,12/19/16      ... 

292.9 

292.25 
292  .2 
292  .2 
.      ...       292  .45 

12/10/16 

I2/I9/l6 

292  .5 

291  .95 
291  .9 

Average  deflection 

.     36.63  mm. 

Deflection. 
42  .50 

42.48 
42.51 
42.51 

Lowering  (corr.). 
k  =  0.005109 

Date. 
I2/I/I6    

0.6934  M  MA 

Zero. 
290.05 

0.1863  mm. 

NNITE. 
Reading. 
332-55 
332-5 
332.45 
332.1 
332  .15 
332.1 
332.2 
332-1 
333-35 
333-3 
333-3 
332.9 
332.8 
332.9 

Zero. 

289.95 
289.95 

289.7 
289.65 
289.6 
290.8 
290.8 

290.3 
290.35 

I2/I/I6 

290.0 
290.05 

I2/2/I6 

I2/2/I6 

290  .4 

290.4 

16 
0.6934  M  MANNITE  (Continued). 

Date.  Zero.  Reading.  Zero  Deflection. 

I2/3/I6 290.0  332.5 

290.0  332.6  289.95 

290.05  332.5  290.05     42.52 


Average  deflection 42  . 50  mm. 

Lowering  (corr.) o .2165  mm. 

k  =  0.005109 


0.7927  M  MANNITB. 

Date.  Zero.  Reading.  Zero.  Reading.  Deflection. 

12/16/16 293.1  341-75 

293.2  341.8      293.1 

293.2  341-8      293.2       ...        48.62 

I2/l6/l6 293.4  342.0 

293.4  342.0 

293-35     342.05     293.5       ...        48.61 
I2/I6/I6 292.0      340.9 

292 .o    340.8 

292  .o    340.8    292 .05 

340.85  292.0  ...        48.83 

12/17/16 340.9  292.15  340.9 

340.95  292.1  340.95 

341-0  292.1  340.95      48.82 

I2/I7/I6 292.8      341.6 

292-75    341-5 
292 .8     341 .6 

341-7     292.85 

341-6     292.85     ...       48.79 
12/18/16 292.9     341.6 

292.95    341-5      ... 
341 .45    293.0 
341-5     293.85     ...       48.56 

12/18/16 292.8     341.4 

292.8     341-55    292.7 
341-65    292.75 
341-55    292.8 
341  -55    292.7      .  .  .       48.78 

i<2/i9/i6 292.25    341-0 

292.25    341.0 

341.0     292.25  48.75 

12/19/16 292.45    34I-I 

292.5  34i  -15 

34I-I5         292.45  ...  48.66 


Average  deflection 48  . 71  mm. 

Lowering  (corr.) o  .2469  mm. 

k  =  0.005109 


17 
0.8913  M  MANNITE. 

Date.  Zero.  Reading.  Zero.  Deflection. 

12/9/16 289.95      344-9 

289.9       344.85 

344.85      289.95       54-94 

12/10/16 289.4      344-35 

289.45     344-25      289.5 

344-3  289.4  54-86 

12/11/16 295.2      349-95 

295.25     350.05 

350.0  295.2  54.78 

12/11/16 295.7  350.5 

295-7      350.6 
295-75     350.65 

350.55      295.75      54.85 

12/11/16 295.0      349-9 

295-0  3498 
349-9 
3499  295.0  54-88 


Average  deflection 54-86  mm. 

Lowering  (corr.) o  .2772  mm. 

k  =  0.005109 


0.8922  M  MANNITE. 

Date.                                                       Zero.  Reading.  Zero.        Reading.        Deflection. 

IO/II/I6 7.0  62.1  ..               ..,. 

7 .O  62  .O  . .               ....               ... 

7.0  62.1  55.03 

10/13/16 3-9  59-0  .,.. 

39  59-0 

4.0  59.0 

58.95         3-95  55  05 

10/14/16 2.2  57.2  ..  .... 

2.1  57.1 

2-2          57-2  55-00 

IO/I6/I6 2.0  57.0  ..  .... 

2.0  57-05  I.Q  

57-0  1.9  5507 

10/18/16 2.9         57.95 

2-9         57-95         3.0 

57.85         3.0  *  54  97 

10/19/16 2.0         57.1 

2.0         57.05 

57-05         2.0  55.07 


General  average .  . ,     55  .03  mm. 

Lowering  (corr.) o  .2792  mm. 

k  =  0.005080 


18 
0.9908  M  Mannite. 

Date.  Zero.  Reading.  Zero.         Deflection  (mean). 

II/I7/I6  2.95  63.9 

2.95  63.9 

63  .  85      2.9       60  .  95 
11/18/16      2.1       63.05 

63.05       ..        ... 
63.05      2.1       60.95 
11/19/16      1.15      62.1 

1.05      62.05      1.05 

62.05  I.O5      60.99 
11/20/16      2.95      64.0       2.9 

64.0  3.0 

64.0  3.0       61.04 
11/20/16      2.65     '63.7 

63.7  2.7 

63.6  2.65      60.99 

Average  deflection  ................................     60.  98  mm. 

Scale  corrected  ...................................     61  .  20  mm. 

Lowering  (corr.)  .............      =  o.  3109  mm. 

Maximum  deviation  .........      =  0.0004  mm. 

k  =  0.005080 

TABLE  II. 
Summary  of  Data. 

G  =  g.  of  mannite  per  1000  g.  of  water  (in  vacuo). 
M  —  concentration  in  moles  per  1000  g.  of  solvent. 
s  —  scale  deflection  in  mm. 

po-pi  =  vapor  pressure  lowering  in  mm.  mercury  (mercury  corr.  to  o°). 
K  =  d/2D. 

Calc.  =  lowering  calculated  according  to  Raoult's  law. 
Diff.  =  difference  between  calculated  and  observed  lowerings. 


.        ..     . 

G.     M.      s.   p0—  />i.feX10-«.  Calc.  Diff.   X10-«.  n/N  +  n      M.  O.  P. 

17-930  0.0984   6.06  0.0307  5080  0.03II  0.0004   17-70  17.31  0.3113  2.343 

36.004  0.1977  12.15  0.0614  5°8O  0.0622  0.0008   35.48  17.32  0.3108  4.703 

53.951  0.2962  18.23  0.0922  5080  0.0931  0.0009   53-09  17.37  0.3133  7.040 

71.917  0.3945  24.26  O.I227  5080  0.1239  O.OOI2   70.64  17.37  0.3107  9.392 

89.938  0.4938  30.20  0.1536  5109  0.1547   o.ooii  88.18  17.42  0.3111  11.78 

108.243  0.5944  36.56  0.1860  5109  0.1858  —  0.0002  105.9  17-55  0.3129  14.27 

108.498  0.5958  36.63  0.1863  5109  0.1862  —  o.oooi  106.2  17.55  0.3128  ... 

126.283  0.6934  42.50  0.2^62  5109  0.2164  —  0.6002  123.4  17-56  0.3118  16.61 

J44-357  0.7927  48.71  0.2478  5109  0.2469  —  0.0009  140.8  17.60  0.3126  19.07 

162.332  0.8913  54.86  0.2791  5109  0.2772  —  0.0019  158.0  17.66  0.3131  21.50 

162.485  0.8922  55.20  0.2792  5080  0.2775  —  0.0017  158.2  17.65  0.3129  ... 

180.451  0.9908  61.20  0.3096  5080  0.3076  -  0.0020  175.4    17.65   0.3124  23.88 

Above,  the  complete  data  for  o.i,  0.5  and  i.o  molar  concentrations 
are  given.  A  table  summarizing  all  the  results  for  the  12  concentrations 
studied  is  shown. 


19 

Discussion  of  Results. 

Accuracy  of  the  Method. — Significant  errors  arising  from  a  varia- 
tion in  the  temperature  are  hardly  possible,  as  no  variation  could  be  de- 
tected by  a  sensitive  Beckmann  thermometer  for  days  at  a  time.  The 
chance  errors  of  observation  are  very  small  as  will  be  seen  by  a  considera- 
tion of  probabilities.  Three  readings  at  least  were  always  made  of  the 
zero  point  and  of  each  deflection.  The  average  error  of  the  zero-point 
setting  was  about  0.03  mm.  and  that  of  the  deflection  reading  0.04  mm. 
scale  deflection.  This  gives  an  average  error  of  each  measurement  of 
V(o.o3)2  +  (o.o4)2  =  0.05  mm.,  or  for  5  observations,  o.oi  mm. 
scale  deflection.  The  probability  that  a  given  series  of  observations  will 
be  within  this  range  is  about  4/7.  In  other  words,  under  the  conditions 
of  the  work,  4  times  out  of  7,  the  error  of  the  observation  of  the  lowering 
will  be  within  o.oi  mm.  scale  deflection,  corresponding  to  0.00005  mm. 
actual  lowering.  However,  this  does  not  represent  at  all  the  accuracy 
of  the  method,  for  there  may  be  certain  constant  errors  whose  relative 
values  are  additive  in  calculating  the  final  error,  i.  There  may  be  a 
slight  amount  of  air  present.  2.  There  is  a  possibility  that  the  surface 
concentration  of  the  solution  is  not  entirely  overcome  by  stirring  the  solu- 
tion during  the  reading.  Altogether  it  is  evident  that  the  method  is 
limited  in  its  accuracy  by  these  factors  and  not  by  errors  of  observation; 
viz.,  (a)  measuring  the  deflection  and  (b)  analyzing  the  solution.  The  2 
separate  determinations  at  o .  6  and  at  o .  9  M  with  the  greater  variation 
in  the  latter  case  of  only  0.0002  mm.  serve  as  a  striking  confirmation. 
It  is  believed  that  the  values  in  Table  II  are  correct  within  0.0006  mm. 

Raoult's  Law. — Table  II  shows  a  summary  of  the  results  and  gives 
the  deviation  from  Raoult's  law,  the  validity  of  which  has  been  supported 
from  theoretical  considerations  by  van  Laar,  G.  N.  Lewis  and  others. 

In  calculating  the  theoretical  lowering  the  equation  — i-i  =  

po  N  +  n 

was  used,  where  p0  is  the  vapor  pressure  of  the  pure  solvent  at  the  same 
temperature,  pi  the  vapor  pressure  of  the  solution,  n  the  number  of  moles 
of  solute,  and  N  the  number  of  moles  of  solvent.  p0  has  been  accurately 
determined  by  Holborn  and  Henning  and  by  Scheel  and  Heuse,  who  give 
the  value  17.539  mm.  The  agreement  of  lower  ings  thus  calculated  with 
experimental  values  is  much  closer  than  when  the  old  form  of  Raoult's 

law  is  used,  P°  ~  ^  =  -.     It  will  be  seen  from  Col.  i,  Table  II  that  the 

po  N 

observed  values  are  increasingly  smaller  than  those  calculated  until  a 
maximum  positive  deviation  is  reached  at  about  o .  4  M.  At  about  o .  6  M 
the  calculated  and  observed  values  are  the  same,  and  it  is  not  until  a 
higher  concentration  is  reached  that  there  is  a  marked  negative  devia- 


20 


tion  from  Raoult's  law.  However,  although  the  deviation  in  the  range 
o.i  to  o.8M  is  never  much  greater  than  the  0.0006  mm.  claimed  as 
the  accuracy  of  the  method,  it  must  be  emphasized  that  the  results  are 
relatively  accurate  enough  to  allow  us  to  draw  some  conclusions  from 
these  deviations. 

.  In  order  to  facilitate  comparison  and  to  magnify  the  deviations  the 
value  of  the  lowering  may  be  divided  by  the  concentration.  Hence  it  is 
often  the  custom  to  examine  vapor  pressure  results  in  the  light  of  the 


n 


N+n 
in  mm. 


17.90 
17.70 
17-50 
17.30 
17.10 
16.90 
16.70 


o.o 


0.7        0.8 


0.9 


>.i        0.2         0.3        0.4        0.5         0.6 
Cone,  in  Mols.  per.  1000  g.  of  water. 

Fig.  4. — Upper  Curve — Molecular  lowering  of   mannite  solutions  at  20°  C.     Lower  Curve — 
The  ratio  of  the  vapor  pressure  lowering  to  the  molar  fraction. 

molecular  lowering  value,  (p0  —  pi)/M,  and  for  that  reason  this  value 
has  been  plotted  against  concentration  hi  Fig.  4  (upper  curve).  How- 
ever, this  function  has  no  theoretical  significance,  as  will  be  seen ;  since 


Po  —pi 


the  hiolecular  lowering, 


N  +  n 


po  —  pi  _      Po 

n         ~  n  +  N' 
n,  is  a  decreasing  one,   with  respect  to  n. 


The  function,  p0/N  +  n,  is  a  decreasing  one,  with  respect  to  n.  It 
seems  that  it  is  often  thought  that  molecular  lowerings  should  be  con- 
stant, but  for  an  ideal  solution  the  molecular  lowering  curve  is  concave 
downward,  only  slightly,  however,  in  dilute  solutions.  Thus  it  is  evi- 


21 

dent  that  conclusions  drawn  from  the  molecular  lowering  curve  may  be 
misleading. 

It  is  more  logical  to  calculate  the  value  of  the  lowering  divided  by  the 
mol  fraction,  which,  according  to  Raoult's  law,  is  a  constant,  viz.,  the 
vapor  pressure  of  water  at  the  temperature  in  question. 


N  +  n 

This  function  has  a  real  meaning.  The  value  of  this  function  is  plotted 
against  concentration  in  Fig.  4  (lower  curve).  An  examination  of  the 
curve  gives  one  a  clear  and  accurate  idea  of  the  behavior  of  mannite 
solutions.  The  smoothness  of  the  curve  in  the  dilute  region,  where  a 
difference  of  o.ooi  mm.  would  bring  a  value  quite  out  of  line,  indicates 
the  normal  character  of  aqueous  mannite  solutions  up  to  0.5  M,  above 
which  slight  irregularities  begin.  The  rise  in  the  curve  in  the  higher  con- 
centrations may  be  attributed  to  hydration.  It  is  unfortunate  that  we 
are  limited  in  further  investigation  by  the  solubility  of  this  substance. 

Von  Babo's  Law  and  the  Heat  of  Dilution.—  The  temperature  coeffi- 
cient of  the  vapor  pressure  of  solutions  is  of  interest,  and  for  this  purpose 
comparison  of  the  results  at  20°  with  those  at  other  temperatures  will 
be  made.  There  are  no  data  of  sufficient  accuracy  on  the  vapor  pressures 
of  mannite  solutions  at  other  temperatures,  and  we  resorted  to  indirect 
comparison  by  means  of  boiling-point  and  freezing-point  data.  Loomis1 
found  that  the  molecular  freezing-point  lowerings  of  mannite  solutions 
are  perfectly  constant.  The  accurate  freezing-point  work  of  Adams,2 
using  very  dilute  solutions,  has  shown  Loomis  to  be  slightly  in  error,  but 
this  is  negligible  for  the  present  comparison.  The  most  concentrated 
solution  measured  by  Hall  and  Harkins,3  using  Adams'  method,  was  o  .  1  197 
and  they  confirmed  closely  the  lowering  found  by  Loomis.  Recently 
Braham4  has  determined  the  lowering  of  2  concentrations  of  mannite 
solutions,  obtaining  value  slightly  higher  than  those  of  Loomis. 

The  relation  between  the  freezing-point  lowering  and  the  vapor  pressure 
of  a  solution  is5 


1  Loomis,  Z.  physik.  Chem.,  32,  599  (1897). 

*  Adams,  /.  Am   Chem.  Soc.,  37^  481  (1915). 

8  Hall  and  Harkins,  ibid.,  38,  2658  (1916). 

4  Braham,  ibid.,  41,  1707  (1919). 

6  This  expression  is  often  deduced  simply  from  the  equation  of  Clausius-Clapeyron 
for  the  variation  of  the  vapor  pressure  of  water  with  the  temperature  and  a  similar 
one  for  ice,  since  at  the  freezing-point  of  a  solution  its  vapor  pressure  is  equal  to  that  of 
ice. 


22 

where  LF  is  the  latent  heat  of  the  solvent  and  T0  and  TF  are,  respectively, 
the  freezing-points  (absolute)  of  solvent  and  solution.  Assuming  that 
Lp  is  independent  of  temperature  the  right-hand  member  becomes 

—  —  ,  where  t  is  the  lowering.     However,  it  is  known  that  the  heat  of 
RT0Tp 

fusion  decreases  with  lowering  temperature  and  it  is  necessary  to  intro- 
duce a  slightly  different  expression  to  take  care  of  this.  This  variation 
is  fundamentally  the  variation  of  the  specific  heat  of  ice,  and  Juttner  ! 
puts,  LF  =  L0  -j-  a(TF  +  ro),  where  LF  and  L0  are  the  heats  of  fusion 
at  Tp  and  T0  and  a  =  S  —  S',  the  difference  between  the  specific  heats 
of  water  and  ice  at  TF.  This  gives  the  expression 

p0       M  [Lo    t  (  t  \]  m 

*»  —  =  -5-  hr  ^F  +  a  ln  (  l  +  ^  )  •  (I) 

pi        R   LTo  TF  \         TF/J 

He  calculated  the  values  of  In  p0/p  for  mannite  solutions  using  L0  =  80.7 
and  a  =  o  .  504  cal.  The  heat  of  fusion  and  the  specific  heat  of  ice  have 
since  been  accurately  determined  by  Dickinson  and  Osborne,2  who  ob- 
tained Lo  =  79.67  cali5°  and  S'  =  0.5052  cali5°.  Recalculating,  using 
these  figures,  R  =  1.985  and  5  =  1.007,  values  about  1.5%  lower  are 
obtained  and  are  given  in  Column  4  of  Table  III. 

Callendar3  has  treated  this  question  similarly  but  has  included  also 
the  variation  of  the  specific  heats  with  temperature.     The  expression  is 

In  £»  =  ^L  +  J-  r  (S-S')dT-r  (S  -S')  *£. 


"The  specific  heat  of  water  is  not  known  accurately  below  o°  but  the  inte- 
grals are  solved  by  making  different  assumptions  as  to  the  variation  of 
5  —  S'  with  temperature.  Nernst4  states  that  this  varies  inversely  with 
the  temperature  just  below  o°.  Callendar's  final  expression  on  this  basis 


T,  7>\ 

T  Tj 


p'  RTPTo  R  \TF  IF 
Values  calculated  by  this  equation  differ  only  slightly  from  those  from 
Equation  I,  and  are  given  in  Column  5  of  Table  III.  It  was  also  found 
that  the  simplified  expression,  proposed  by  Callendar 

po       ML0t 
In  —f  =  =  0.9695  £ 

gives  values  practically  identical  with  those  of  his  rigid  expression,  since  t 
is  never  greater  than  i  °. 

1  Juttner,  Z.  physik.  Chem.,  38,  no  (1901). 

2  Osborne,  Bur.  Standards,  Sci.  Paper  248  (1918). 

3  Callendar,  Proc.  Roy.  Soc.,  (A),  80,  446  (1908). 
*  Nernst,  Trans.  Faraday  Soc.,  6,  117  (1910). 


23 


Vapor  pressure  ratios  may  be  obtained  from  boiling-point  elevation 
values  by  application  of  the  same  fundamental  equation,  but  a  surer 
method  is  to  find  the  atmospheric  pressure  from  the  boiling  temperature 
of  the  pure  solvent.  This  becomes  pi  the  vapor  pressure  of  the  solution, 
when  the  boiling  temperature  is  raised  slightly  above  that  of  the  solvent. 
Then  the  vapor  pressure  of  the  pure  solvent  for  that  final  temperature  is 
found  by  the  use  of  tables.  This  gives  p0  and  pi  at  the  same  tempera- 
ture. Juttner  has  calculated  the  values  of  In  p0  /pi  from  Beckmann's1  data 
which  are  giren  in  Column  7  of  Table  III,  while  the  observed  values  of 
the  present  authors  are  given  in  Column  6. 

TABUS  III. 

Comparison  of  Vapor  Pressure  Ratios  at  20°  with  those  Obtained  from  Freezing-and 

from  Boiling-Points. 


F.  pt.  lowering,  t. 


M. 

O.IOI3 
O.I3I 
0.2061 

0.268 

0.2709 

0.5323 

0.537 

0.546 

0.801 

1.018 


Obs. 

o.  1874 

0.3807 

0.505 
0.9835 

I.OI9 


Caic. 
0.1857 

0.3776 

o . 4962 

0-9737 
1.005 


In 

Po/Pl. 

0°- 

-t. 

I. 

II. 

20°. 

100°  +  <'. 

0.00181 

0.00182 

O.OOlSo 

.  .  . 

0.00233 

0.00235 

o  .  00368 

0.00369 

o  .  00366 

.  .  . 

0.00479 

o  .  0045  i 

0.00488 

o  .  00490 

0.00481 

o  .  00950 

0.00953 

0.00945 

0.00957 

o  .  0095  i 

o  .  00985 

o  .  00988 

0.00974 

0.01438 

0.01448 

0.01902 

0.01915 

The  calculated  values  of  /,  given  in  Column  3,  are  obtained,  using  Cal- 
lendar's  equation,  from  the  values  of  In  p0  /pi  determined  experimentally  at 
20°  by  the  authors,  assuming  that  this  function  is  the  same  at  the  freez- 
ing-point or  is  independent  of  temperature.  Von  Babo's  law  states  that 
the  relative  lowering  of  vapor  pressure  is  independent  of  the  tempera- 
ture. And  KirchhofFs  equation  for  the  heat  of  dilution  is  a  quantitative 
statement  of  the  deviations  from  Von  Babo's  law. 
H  =  RT*b/t>T(lnp0/pi). 

H  is  the  heat  of  dilution  and  is  here  defined  as  the  heat  which  must  be 
added  to  keep  the  temperature  constant  when  one  gram  of  solvent  is 
added  to  an  infinite  amount  of  solution.  Von  Babo's  law  is  thus  a  special 
case  of  Kirchhoff's  equation  and  merely  states  that 

5/5T  (In  po/pi)  =  o. 

Hence  the  function  Inp0/pi  is  a  very  convenient  one  to  use  in  dealing 
with  the  variation  of  vapor  pressure  with  temperature. 

It  is  seen  that  the  calculated  freezing-point  lowerings  are  slightly  smaller 
.than  the  observed,  which  deviation  is  roughly  proportional  to  the  concen- 
1  Juttner,  Z.  physik.  Chem.,  6,  459  (1890). 


24 

tration.  Von  Babo's  law  does  not  hold  exactly,  therefore,  and  the  In  p0  /pi 
curve  for  o°  lies  slightly  over  that  for  20°  and  the  heat  of  dilution  is  nega- 
tive. The  In  p0/pi  values  at  100°  lack  smoothness  as  the  lowest  concen- 
tration is  somewhat  out  of  line,  but  the  smoothed  curve  lies  under  the  20° 
curve  for  the  lower  concentrations  (below  o.8M),  showing  a  decrease  in 
In  po/pi  from  o°  to  20°  to  100°.  For  the  lowest  concentration  the  values 
of  this  function  agree  quite  closely  for  o°,  20°,  and  100°,  which  means  a 
very  small  (negative)  heat  of  dilution.  Pratt1  has  measured  the  heat 
evolved  when  solutions  of  mannite  are  diluted,  but  the  data  are  empirically 
expressed  and  do  not  admit  of  quantitative  comparison.  However,  his 
observations  are  in  qualitative  agreement  with  the  deduction  as  regards 
sign  and  order  of  magnitude  of  the  heat  by  dilution.  The  mean  heat  of 
dilution  between  o°  and  20°  for  a  0.5  M  solution  is  roughly  —  0.5  cal, 
using  the  data  in  Table  III  and  KirchhofFs  equation.  For  the  concen- 
trations 0.8  and  i.oM,  the  Inp0/pi  at  1  00°  are  greater  than  those  at  20°, 
indicating  that  the  heat  of  dilution  changes  sign  with  increasing  concentra- 
tion, a  not  unusual  phenomenon.  It  is  significant  that  this  takes  place  in 
the  same  concentration  as  that  in  which  the  deviation  from  Raoult's  law  is 
marked. 

Vapor  Pressure  and  Osmotic  Pressure.  —  The  relation  between 
osmotic  pressure  and  vapor  pressure  has  been  discussed  by  a  number  of 
authors,  using  different  methods  and  resulting  in  a  number  of  equations 
which  differ  only  slightly  according  to  the  conditions  and  definitions 
chosen.  The  integral  equation  of  A.  W.  Porter2  covers  all  of  these  and 
is  an  expression  for  solutions  of  any  compressibility  and  under  any  hydro- 
static pressure.  Introducing  the  limits  corresponding  to  the  conditions, 
neglecting  compressibility  and  using  the  gas  law  for  the  vapor  pressure 
he  obtains. 


, 

V,       fi 

Vs  is  the  increase  in  volume  when  one  gram  of  solvent  is  added  to  a  large 
amount  of  solution,  and  is  a  function  of  the  density.3  This  was  found  to 
be  a  correction  of  about  0.1%.  The  calculated  values  of  the  osmotic 
pressure  are  given  in  Column  10,  Table  II.  Final  direct  measurements 
of  the  osmotic  pressure  have  not  been  made,  but  will  be  the  object  of  a 
futufe  investigation. 

Summary. 

i.  The  vapor  pressure  lowerings  of  aqueous  mannite    solutions    have 
been  determined  over  the  range  of  its  solubility. 

1  J.  Franklin  Inst.,  185,  663  (1918). 

2  Porter,  Proc.  Roy.  Soc.,  (A.},  79,  519  (1907). 

3  Gouy  and  Chaperon,  Ann.  chim.  phys.,  [6]  12,  384  (1887). 


25 

2.  The  presence  of  dissolved  air  as  a  source  of  error  has  been  eliminated 
by  a  new  method  of  preparing  the  solutions. 

3.  A  mean  deviation  from  Raoult's  law  of  only  0.0006  mm.  is  observed 
up  to  0.8  M  concentration. 

4.  By  comparison  with  freezing-point  lowerings  it  is  found  that  In  p0/pi 
decreases  with  the  temperature  or,  the  heat  of  dilution  is  a  small  nega- 
tive value  for  concentrations  up  to  o .  5  M.     Comparisons  with  boiling- 
point  determinations  show  that  this  changes  to  a  positive  quantity  in 
the  higher  concentrations. 


BIOGRAPHY. 

The  author  of  this  dissertation  was  born  in  Kentucky,  January  25, 
1895.  He  received  his  early  education  in  the  public  schools  of  Lexington, 
Ky.,  and  graduated  from  Centre  College,  Danville,  Ky.,  in  1914,  receiving 
the  degree  of  Bachelor  of  Arts.  In  the  fall  of  1914,  he  entered  the  Johns 
Hopkins  University  as  a  graduate  student  in  Chemistry,  taking  Physical 
Chemistry  and  Mathematics  as  subordinate  subjects.  During  the  years 
1915-6  and  1916-17,  he  was  appointed  Hopkins  Scholar. 


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